Tomography of memory engrams in self-organizing nanowire connectomes

Self-organizing memristive nanowire connectomes have been exploited for physical (in materia) implementation of brain-inspired computing paradigms. Despite having been shown that the emergent behavior relies on weight plasticity at single junction/synapse level and on wiring plasticity involving topological changes, a shift to multiterminal paradigms is needed to unveil dynamics at the network level. Here, we report on tomographical evidence of memory engrams (or memory traces) in nanowire connectomes, i.e., physicochemical changes in biological neural substrates supposed to endow the representation of experience stored in the brain. An experimental/modeling approach shows that spatially correlated short-term plasticity effects can turn into long-lasting engram memory patterns inherently related to network topology inhomogeneities. The ability to exploit both encoding and consolidation of information on the same physical substrate would open radically new perspectives for in materia computing, while offering to neuroscientists an alternative platform to understand the role of memory in learning and knowledge.

The circled area 1 in panel c refers to the temporal sequence where the synaptic pathway connecting terminals 7 and 9 is directly stimulated.As can be observed, besides changes in the effective conductance of the directly stimulated pathway (7,9), significant changes in the effective conductance were observed also in pathways (7,14) and (2,9), while almost no changes were observed in pathway (2,14).This behavior is related to the spatial location of neuron terminals.Indeed, while pathways (7,14) and (2,9) share neuron terminals with the directly stimulated (7,9) pathway, the pathway (2,14)  involves peripheral areas of the network with respect to the directly stimulated area.Similarly, in the circled area 2 where the pathway (2,14) is directly stimulated with paired pulses, negligible changes in the peripheral synaptic pathway (7,9) can be observed, while larger changes are observed in pathways (2,9) and (7,14).These examples show the dependence of heterosynaptic plasticity effects on the spatial location of neuron terminals due to the functional connectivity of the memristive network.The value of the pristine conductance of each grid-graph edge  0 is estimated by interpolating the median conductance of the ERT map resulting from the grid-graph model and the median conductance of the experimental map reported in Figure 2d.In the pristine state, each edge of the grid-graph was assigned to the same  0 value under the assumption of a homogeneous NW network.

Supplementary
As a first step, the grid-graph model was initialized by imposing a  0 value of conductance to each edge.Then, the transresistance pattern and the corresponding impedance matrix were acquired to obtain the conductivity map of the grid-graph model by means of ERT reconstruction.Subsequently, the median conductance of the pixels of the map was calculated.The same procedure was repeated for different values of  0 , unveiling a linear relationship in between the median conductivity of the reconstructed map and the  0 edge conductance.By exploiting a linear interpolation of data, the  0 value of edges was extrapolated such that the median conductance of the simulated conductivity map matches well with the conductivity map reconstructed from experimental data as reported in Figure 2. to the homogeneous sample that reflects in a less homogeneous spatial distribution of conductivity across the network.The non-homogeneous network, that is characterized by a lower median conductance, is characterized by larger percentage variations of conductivity over the network.

Parameters Value
min 2,1 mS *Average number of synaptic density in adult life cells 21,22 .The consistency of this approach is supported also by the observation that the emergent memristive behavior of self-assembled networks can be described by an equation where complexity can be reabsorbed into the effective parameters of a single memristive element, as recently theoretically shown through a mean-field theory approach 23 .
Previous results demonstrated that this modelling approach is able to emulate main features of the emergent memristive functionalities of NW networks and represent a versatile model for exploiting computing implementation strategies 17,24,25 the measurement accuracy which is typical of laboratory grade instrumentation is small. 27The assessment of the final ERT image accuracy is an open problem.The accuracy of the conductivity values given by the reconstructed maps has been validated, also by comparison with other measurement techniques [10], [11], on reference samples.about 800 frames per second image reconstruction rate with real time reconstruction. 36In this context, the measurement speed of the set of electrical measurements required for ERT reconstruction of NW networks can be increased by exploring measurement protocols in the AC regime.

Supplementary Figure S2 |
Photograph of the contact fixture for multiterminal electrical characterization.The sample, loaded on Figure S5 | Experimental transresistance pattern from adjacent pattern measurement scheme.Source current ( source ) pattern, corresponding sense voltage ( sense ) pattern and transresistance pattern.Measurements were performed by applying a voltage of 10 mV to adjacent source terminals and measuring the corresponding  source , while measuring  sense across other pairs of adjacent terminals.The source configuration is labelled at the top.Supplementary Figure S6 | Reproducibility of the ERT measurement pattern.Mean and standard deviation (× 100) of measured ERT patterns evaluated by repeating the ERT measurement protocol 10 times on a NW network in the pristine state.A standard deviation in transresistance values < 0.5 % was observed, showing that the measurement protocol maximizes the signal-to-noise ratio while preventing the onset of sample alterations.Supplementary Figure S9.Experimental investigation of the spatial resolution of the ERT setup.a. Fluorinated tin oxide (FTO) thin film with a thin linear cut (white marker of about 50 m).Before the linear cut, the FTO sample was characterized by a uniform conductivity of 150 mS 2 .b. Conductivity dip observed in the diagonal conductivity profile of the sample (in the direction of the black arrow in the map of panel a), where the full width at half maximum corresponds to ≈ 1.7 mm.Details on ERT spatial resolution in Supplementary Note 5. Supplementary Figure S10 | Extraction of grid-graph model parameters in the pristine state.
Figure S12 | Long-term stability of NW networks.a. Transresistance pattern of an Ag NW network after deposition and b. evolution over time of transresistance values of all the 208 configurations, monitored by placing the ERT setup in a hermetically closed box to limit the interaction with the environment.After initial stabilization, transresistance values of the multiterminal NW network tend to stabilize to near constant values and no network failures were observed after 20 days.Supplementary Figure S13 | Mapping dynamic formation of synaptic pathways across the NW network connectome.a. Schematic representation of the multiterminal configuration with highlighted terminals of the directly stimulated synaptic pathway and b. experimental and simulated evolution of the effective conductance in between the selected pair of contacts during potentiation (detail of Figure 3b).c.Evolution of the memristive network by grid-graph modelling (red intensity is proportional to the edge conductance, blue intensity is proportional to the node voltage), d. corresponding simulated differential impedance matrices and e. corresponding simulated differential conductivity maps by ERT reconstruction during stimulation (Supplementary Movie 2).The gridgraph model and the reconstructed maps enable direct investigation of the synaptic potentiation dynamics at the macroscale, showing the gradual formation of a potentiated conductive pathway growing over time starting from the stimulated contacts along the electric potential gradient.Supplementary Figure S14 | Emergent behavior of the NW network connectome at the micro/nanoscale.a. NW network topology simulated by dispersing 1D objects (1800 NWs) on a 2D plane (500 × 500 µm 2 ), where red dots represent NW midpoints while blue dots represent NW junctions, and b. corresponding graph representation.c.Electrical backbone of the network when stimulated in between source (red marked node, upper left) and ground node (black marked node, bottom right).d.Corresponding visualization of the potential distribution across graph nodes when a voltage difference is applied between these nodes.e. Corresponding voltage distribution across the 2D plane.f.Activation pattern of the network after stimulation in between source and ground nodes with a voltage pulse, showing the emergence of a conductive pathway composed of multiple branches that connects source and ground nodes.Red intensity is proportional to edge conductance, blue intensity is proportional to node voltage.Supplementary Figure S15 | Comparison of the homogeneous and the non-homogeneous network.a. Impedance matrix and b. conductivity map of the high density nearly homogeneous NW network, c. map of the percentage variation of conductivity across the network with respect to the median conductance value of the network (median conductance of 15,8 mS) and d. corresponding pixel histogram of conductance variations.e. Impedance matrix and f. conductivity map of the nonhomogeneous NW network, g. map of the percentage variation of conductivity across the network with respect to the median conductance value of the entire network (median conductance of 5,9 mS) and h.corresponding pixel histogram of conductance variations.A comparison of the impedance matrices shows a less uniform impedance matrix in case of the non-homogeneous network compared

Table 2 . Comparison of ERT with other characterization techniques for direct visualization of conductive pathways in self-organizing nanonetworks.
Not specified, estimation based on technique properties.▲ Acquisition time scales quadratically with the scanning area in scanning techniques Supplementary *